1880.] Notes of Observations on Musical Beats. 



521 



m—n. Hence all beats heard are beats of simple partial tones, however 

 compound may be the tones which contain them. This agrees 

 thoroughly with my observations. 



Tuning-forks are comparatively simple but always possess an audible 

 second partial or octave, and sometimes higher partials still, capable 

 of being so reinforced by resonance jars properly tuned to them, that 

 beats can be separately obtained from them and counted. This is a 

 matter of great importance in the construction of a tuning-fork 

 tonometer. When the tone is very compound, as in the case of bass 

 reeds (especially those of Appunn's tonometer, furnished with a 

 bellows giving, when properly managed, a perfectly steady blast for 

 an indefinite length of time), beats can be obtained and counted from 

 the 20th to the 30th and even the 40th partial, without any reinforce- 

 ment by a resonance jar. 



Taking tuning-forks first, I find it advantageous to hold the beating- 

 forks over one or two resonance jars, tuned, by pouring in water, to 

 the pitch of the partial to be observed, whether it be the prime of 

 both or the prime of one and the second (or octave) of the other. 

 There may be small differences, but I have not found any difference 

 appreciable by my methods of observation in the number of beats in 

 a second, whether the resonance jar is the same or different for the 

 two forks, and whether it is exactly or very indifferently tuned to each 

 fork, but a tolerably accurate tuning much improves the tone and 

 length of the beat. In that case the resonance jar practically quenches 

 all other partial tones, and the beats are distinctly heard as loudnesses 

 separated by silences. If no jar is used, the other partials are heard. 

 In the case of the octave, the low prime becomes a drone and fills up 

 the silences. In the case of beating primes, the octaves, which are 

 beating twice as fast, tend to confuse the ear. Sometimes the second 

 partial of a fork is so much stronger than the prime, that when the 

 fork is applied to a sounding-board, only the octave is heard, which is 

 inconvenient. This is entirely avoided by the resonance jar. Beats 

 being a case of interference, the amplitude of the beating partials 

 should be equalised as much as possible. With two forks of very 

 different size and power, it is easy to regulate the amplitude by hold- 

 ing the louder fork further from the jar. Otherwise the beats become 

 blurred and indistinct. For powerful reeds or organ pipes, beating 

 with forks, it is best to go to a considerable distance from the reed or 

 pipe and hold the fork close to the ear or over a jar. I find 30 or 

 40 feet necessary for organs ; in Durham Cathedral, where the 

 pressure of wind was strong and my forks weak, I found 60 or 70 feet 

 distance much better. As I was not able latterly to go to a distance 

 from Appunn's reed tonometer, having to pump it myself, I found it 

 impossible to count the primes of the upper reeds by the octaves of 

 my forks, which were completely drowned. 



